247:
158:
59:
288:
187:
281:
312:
83:
274:
307:
190:
26:
254:
226:
216:
17:
189:. This property defines one sense in which an additive monoid can be as unlike an additive
230:
166:
258:
301:
204:
246:
221:
21:
163:
This means that the only way zero can be expressed as a sum is as
153:{\displaystyle (\forall a,b\in M)\ a+b=0\implies a=b=0\!}
262:
169:
86:
29:
77:if nonzero elements do not sum to zero. Formally:
205:"Tensor products of structures with interpolation"
181:
152:
53:
149:
282:
8:
289:
275:
133:
129:
220:
168:
85:
28:
193:as possible: no elements have inverses.
7:
243:
241:
90:
14:
245:
209:Pacific Journal of Mathematics
130:
108:
87:
48:
30:
1:
261:. You can help Knowledge by
203:Wehrung, Friedrich (1996).
329:
240:
222:10.2140/pjm.1996.176.267
54:{\displaystyle (M,0,+)}
313:Abstract algebra stubs
257:-related article is a
183:
154:
55:
184:
155:
56:
167:
84:
27:
182:{\displaystyle 0+0}
179:
150:
51:
270:
269:
113:
320:
308:Semigroup theory
291:
284:
277:
255:abstract algebra
249:
242:
234:
224:
188:
186:
185:
180:
159:
157:
156:
151:
111:
60:
58:
57:
52:
18:abstract algebra
328:
327:
323:
322:
321:
319:
318:
317:
298:
297:
296:
295:
238:
202:
199:
165:
164:
82:
81:
25:
24:
12:
11:
5:
326:
324:
316:
315:
310:
300:
299:
294:
293:
286:
279:
271:
268:
267:
250:
236:
235:
215:(1): 267–285.
198:
195:
178:
175:
172:
161:
160:
148:
145:
142:
139:
136:
132:
128:
125:
122:
119:
116:
110:
107:
104:
101:
98:
95:
92:
89:
61:is said to be
50:
47:
44:
41:
38:
35:
32:
20:, an additive
13:
10:
9:
6:
4:
3:
2:
325:
314:
311:
309:
306:
305:
303:
292:
287:
285:
280:
278:
273:
272:
266:
264:
260:
256:
251:
248:
244:
239:
232:
228:
223:
218:
214:
210:
206:
201:
200:
196:
194:
192:
176:
173:
170:
146:
143:
140:
137:
134:
126:
123:
120:
117:
114:
105:
102:
99:
96:
93:
80:
79:
78:
76:
72:
68:
64:
45:
42:
39:
36:
33:
23:
19:
263:expanding it
252:
237:
212:
208:
162:
74:
70:
66:
62:
15:
63:zerosumfree
302:Categories
231:0865.06010
197:References
71:centerless
131:⟹
103:∈
91:∀
75:positive
67:conical
229:
112:
22:monoid
253:This
191:group
259:stub
227:Zbl
217:doi
213:176
73:or
16:In
304::
225:.
211:.
207:.
69:,
65:,
290:e
283:t
276:v
265:.
233:.
219::
177:0
174:+
171:0
147:0
144:=
141:b
138:=
135:a
127:0
124:=
121:b
118:+
115:a
109:)
106:M
100:b
97:,
94:a
88:(
49:)
46:+
43:,
40:0
37:,
34:M
31:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
